A-TIER art
Escher's Print Gallery — 3Blue1Brown on the complex-analysis loop at its center
100k ft — What is this?
Escher's Print Gallery — 3Blue1Brown on the complex-analysis loop at its center
50k ft — Why care?
3Blue1Brown's 45-minute visual deep dive on M.C. Escher's 1956 lithograph Print Gallery, building on de Smit and Lenstra's 2003 analysis that reveals the self-similar conformal loop and answers what belongs in the picture's blank center.
10k ft — Key takeaways
• De Smit and Lenstra's analysis fills in Escher's blank center
• Great reference for recursive/Droste visual effects
• Print Gallery's warp is a conformal (complex-analysis) map with a self-similar loop
5k ft — Tools & techniques
(no tools tagged)
Droste effect, conformal mapping
1k ft — Deep-dive / try it
New video! This one is on Escher’s “Print Gallery”. This was one of the most visually intensive projects I’ve done, take a look next time you’re looking to sit down with 45 minutes of math and art.
Transcript excerpt
Imagine standing in a gallery, looking at a picture of a boat in a harbor, and the whole world kind of warps as your gaze shifts upwards and to the right, where you see a village on this waterfront. Among the tightly clustered buildings, the world warps even more as your gaze shifts downwards to the entrance of one building, leading to a hallway full of artwork. And at the end of this hall, here you are again, staring at a picture of a boat. This is MC Escher's 1956 lithograph, the print gallery. In a letter that he wrote to his son, Escher called this the most peculiar thing I have ever done. Which for him is saying a lot. In 2003, the mathematicians, Dismitt and Lentstra, offered a delightful analysis of what's really going on in this piece and the mind-bending self-contained loop that Escher managed to achieve. Something that unexpectedly pops out of this analysis is an answer to the question of what exactly should go in the middle of this picture. At first, that might sound like an incoherent question. If you come at it from the upper right, it feels like it should be featuring buildings in the village, but coming at it from the left, it looks more like part of the picture frame. Come at it from below, though, and it feels more fitting to be part of the gallery itself. Somehow, all of the ambiguity about where exactly you are in this whole scene is compressed into that blank circle in the middle.